A kernel-based framework to tensorial data analysis

Signoretto, Marco; Lathauwer, Lieven De; Suykens, Johan A. K.

doi:10.1016/j.neunet.2011.05.011

Cited by 93 publications

(97 citation statements)

References 26 publications

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“…In order to define a similarity measure that directly exploits the multilinear algebraic structure of input tensors, Signoretto et al [2011Signoretto et al [ , 2012 proposed a tensorial kernel which both exploits the algebraic geometry of tensors spaces and provides a similarity measure between the different subspaces spanned by higher-order tensors. Another such kernel is the product kernel which can be defined by N factor kernels, as k(X,…”

Section: Kernel Functions In Tensor Learningmentioning

confidence: 99%

“…One similarity measure between matrices is the so called Chordal distance, which is a projection of the Frobenius norm on a Grassmannian manifolds [Signoretto et al, 2011]. For example, for an Nth-order tensor, X, upon the applications of SVD to its mode-n unfolding, that is,…”

Section: Kernel Functions In Tensor Learningmentioning

confidence: 99%

“…It should be emphasized that such a tensor kernel ensures (provides) rotation and reflection invariance for elements on the Grassmann manifold [Signoretto et al, 2011]. Zhao et al [2013c] proposed a whole family of probabilistic product kernels based on generative models.…”

Section: Kernel Functions In Tensor Learningmentioning

confidence: 99%

See 2 more Smart Citations

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives

Cichocki

Phan

Zhao

et al. 2017

FNT in Machine Learning

191

126

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Section: Kernel Functions In Tensor Learningmentioning

confidence: 99%

Section: Kernel Functions In Tensor Learningmentioning

confidence: 99%

See 1 more Smart Citation

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives

Cichocki

Phan

Zhao

et al. 2017

FNT in Machine Learning

191

126

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“…• Factor kernel (FK) [9]: a matrix unfolding based tensor kernel. The constituent kernels are from the class of Gaussian RBF kernels.…”

Section: Baselines and Metricsmentioning

confidence: 99%

“…Most of conventional kernel methods convert a tensor to a vector (or a matrix), which is then adapted in the kernel modeling [9,10]. However, voxels are often highly correlated with the surrounding voxels in the brain volume.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Tensor Analysis for Whole-Brain fMRI Classification

Ma¹,

He²,

Lu³

et al. 2016

Proceedings of the 2016 SIAM International Conference on Data Mining

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Owing to prominence as a research and diagnostic tool in human brain mapping, whole-brain fMRI image analysis has been the focus of intense investigation. Conventionally, input fMRI brain images are converted into vectors or matrices and adapted in kernel based classifiers. fMRI data, however, are inherently coupled with sophisticated spatio-temporal tensor structure (i.e., 3D space × time). Valuable structural information will be lost if the tensors are converted into vectors. Furthermore, time series fMRI data are noisy, involving time shift and low temporal resolution. To address these analytic challenges, more compact and discriminative representations for kernel modeling are needed. In this paper, we propose a novel spatio-temporal tensor kernel (STTK) approach for whole-brain fMRI image analysis. Specifically, we design a volumetric time series extraction approach to model the temporal data, and propose a spatio-temporal tensor based factorization for feature extraction. We further leverage the tensor structure to encode prior knowledge in the kernel. Extensive experiments using real-world datasets demonstrate that our proposed approach effectively boosts the fMRI classification performance in diverse brain disorders (i.e., Alzheimer's disease, ADHD and HIV).

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